Two-pipe Circumference Problem

Please see attached diagram.

I have an Engineering problem where straps are to be placed around two pipes. I know the diameter/radius of both pipes and the distance from centre to centre of both pipes. From this information, can I calculate the total strap length (this will be made up of two arc lengths around each pipe and two straight portions tangential to both pipes)?

I can draw it each time, but it would be useful to have an equation and having failed to work it out myself, I am now intrigued as to whether it can be done!

I looked at it as a problem of lots of right-angled triangles. I know I need to calculate the angle of the straight portions of the strap, but I lost my way a bit. Does anybody fancy having a go?!

I have an Engineering problem where straps are to be placed around two pipes. I know the diameter/radius of both pipes and the distance from centre to centre of both pipes. From this information, can I calculate the total strap length (this will be made up of two arc lengths around each pipe and two straight portions tangential to both pipes)?

I can draw it each time, but it would be useful to have an equation and having failed to work it out myself, I am now intrigued as to whether it can be done!

I looked at it as a problem of lots of right-angled triangles. I know I need to calculate the angle of the straight portions of the strap, but I lost my way a bit. Does anybody fancy having a go?!

Let R be the radius of the larger pipe (includes pipe wall)
Let r be the radius of the smaller pipe.
Let s be the distance separating the two pipes.
theta is the angle at the intersection of the tangents to the pipe (theta in radians):

TotalStrapLength =

.

Last edited by aidan; November 18th 2009 at 11:41 PM.
Reason: Added equation